Problema Solution
Several ancient Chinese books included problems that can be solved by translating to systems of equations. Arithmetical Rules in Nine Sections is a book of 246 prooblems complied by a Chinese mathmatician, Chang Tsang, who died in 152 B.C. Solve the following problem from this bokk: There are a number of rabbits and pheasants confined in a cage. In all, there are 35 heads and 94 feet. How many rabbits and how many pheasants are there?
Answer provided by our tutors
Let R = the number of rabbits and P = the number of pheasants.
Since both rabbits and pheasants have but one head each, then:
1) R+P = 35
Rabbits have four legs each while pheasants have two legs each, so we can write the total number of legs as:
2) 4R+2P = 94
By solving above two equations
R = 35-P :
4R = 140-4p and substitute this for 4R in equation 2, then solve for P.
140-4P+2P = 94 Simplify.
140-2P = 94 Subtract 140 from both sides.
-2P = -46 Divide both sides by -2.
P = 23 There are 23 pheasants.
R = 35-P
R = 35-23
R = 12 There are 12 rabbits.